Algebraic fibre spaces with strictly nef relative anti-log canonical divisor
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909278421385216 |
|---|---|
| author | Liu, Jie Ou, Wenhao Wang, Juanyong Yang, Xiaokui Zhong, Guolei |
| author_facet | Liu, Jie Ou, Wenhao Wang, Juanyong Yang, Xiaokui Zhong, Guolei |
| contents | Let $(X,Δ)$ be a projective klt pair, and $f:X\to Y$ a fibration to a smooth projective variety $Y$ with strictly nef relative anti-log canonical divisor $-(K_{X/Y}+Δ)$. We prove that $f$ is a locally constant fibration with rationally connected fibres, and the base $Y$ is a canonically polarized hyperbolic projective manifold. In particular, when $Y$ is a single point, we establish that $X$ is rationally connected. Moreover, when $\dim X=3$ and $-(K_X+Δ)$ is strictly nef, we prove that $-(K_X+Δ)$ is ample, which confirms the singular version of a conjecture of Campana-Peternell for threefolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_05234 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Algebraic fibre spaces with strictly nef relative anti-log canonical divisor Liu, Jie Ou, Wenhao Wang, Juanyong Yang, Xiaokui Zhong, Guolei Algebraic Geometry Complex Variables Differential Geometry 14E30, 14H30, 14J45, 32Q57, 53C22 Let $(X,Δ)$ be a projective klt pair, and $f:X\to Y$ a fibration to a smooth projective variety $Y$ with strictly nef relative anti-log canonical divisor $-(K_{X/Y}+Δ)$. We prove that $f$ is a locally constant fibration with rationally connected fibres, and the base $Y$ is a canonically polarized hyperbolic projective manifold. In particular, when $Y$ is a single point, we establish that $X$ is rationally connected. Moreover, when $\dim X=3$ and $-(K_X+Δ)$ is strictly nef, we prove that $-(K_X+Δ)$ is ample, which confirms the singular version of a conjecture of Campana-Peternell for threefolds. |
| title | Algebraic fibre spaces with strictly nef relative anti-log canonical divisor |
| topic | Algebraic Geometry Complex Variables Differential Geometry 14E30, 14H30, 14J45, 32Q57, 53C22 |
| url | https://arxiv.org/abs/2111.05234 |